# [seqfan] Re: A016910 (6n)^2 and twin primes

apovolot at gmail.com apovolot at gmail.com
Tue Jun 17 00:54:28 CEST 2014

```Hello Olivier - then you could probably incorporate the following from A235644

REFERENCES
Liang ding xiang, problem solving 93#, Bulletin of Mathematics (Wuhan), 6(1992),41. ISSN 0488-7395.

> On Jun 16, 2014, at 5:34 PM, Olivier Gerard <olivier.gerard at gmail.com> wrote:
>
> Dear Mike,
>
> This has already been done under https://oeis.org/A243941.
>
> Olivier
>
>
>
>> On Mon, Jun 16, 2014 at 1:24 PM, Tw Mike <mt.kongtong at gmail.com> wrote:
>>
>> I'm trying to add the solutions to OEIS, see draft/A235644 , not sure if
>> the data 1, 2, 2, 5, 5, 3, 6, 3, 6,  .... is correct.
>> Yours mike,
>>
>>
>> 2014-06-15 18:36 GMT+08:00 Olivier Gerard <olivier.gerard at gmail.com>:
>>
>>> =On Sat, Jun 14, 2014 at 4:47 PM, Tw Mike <mt.kongtong at gmail.com> wrote:
>>>
>>>> Dear seqfans,
>>>>
>>>> It is conjectured that  A016910(n) = p_1 + p_2 + p_3 + p_4, where (p_1,
>>>> p_2) and (p_3, p_4) are twin prime pairs.
>>> Let us be clear. Either you conjecture this by yourself, and you should
>> say
>>> so or
>>> you read about someone else conjecturing and you should give the source.
>>>
>>> For example:  A016910(1) = 36 = 5 + 7 + 11 + 13.
>>>
>>> Also you should check as much as possible before reporting it.
>>>
>>> In general, there seems to be many solutions for each n.
>>>
>>> For instance, before writing this email, I checked up to n=40 that there
>>> was at least one solution for each n, I looked into the sequence of the
>>> number of solutions
>>> to check if it was recorded in the OEIS (it is not), etc.
>>>
>>>
>>>> Are there some research or paper or progress of this conjecture?
>>> As Giovanni already said, what your are discussing implies that there is
>>> infinitely many twin primes.
>>> representations
>>> of numbers by sums of primes, a very active topic, related to the
>> Goldberg
>>> conjecture and
>>> its variants.
>>>
>>> Olivier
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
```